You shouldn't run into any issues when mining either in Linux or in Windows.

If you were playing games, the 6970 would throttle back to match the 6950 so the game would play in sync. When mining however, each card works independently of each other and will go as fast as it can.

"Generation" was an issue for me under Windows, as I was unable to mix 5xxx and 6xxx cards and install proper drivers to get mining. The AMD CrossfireX Compatibility Chart illustrates which combinations are supported.

However this has not been an issue for me in Linux; I have a rig with a 6950 and 5850 and each is mining to capacity.